Large-scale Nonlinear Systems Research Articles

A new numerical path to retrieve isolated branches on large scale nonlinear mechanical systems

A new numerical path to retrieve isolated branches on large scale nonlinear mechanical systems

Rigorous design and economic optimization of reactive distillation column considering real liquid hold-up and hydraulic conditions of industrial device

The liquid hold-up in a reactive distillation (RD) column not only has a significant impact on the extent of reactions, but also affects the pressure drop and hydraulic conditions in the column. Therefore, the liquid hold-up would be a critical design factor for RD columns. However, the existing design methods for RD columns typically neglect the influence of considerable amount of liquid hold-up in downcomers owing to the difficulties of solving a large-scale nonlinear model system by considering downcomer hydraulics, resulting in significant deviations from actual situation and even operation infeasibility of the designed column. In this paper, a pseudo-transient (PT) RD model based on equilibrium model considering tray hydraulics was established for rigorous simulation and optimization of RD plate columns considering the liquid hold-up both in downcomers and column trays, and a steady-state optimization algorithm assisted by the PT model was adopted to robustly solve the optimization problem. The optimization results of either ethylene glycol RD or methyl acetate RD demonstrated that assuming all the liquid hold-up of a stage belonged to the tray will cause significant deviations in the column diameter, weir height, and the number of stages, which leads to not meeting the separation requirements and even operation hydraulic infeasibility. The rigorous model proposed in this study which considers the liquid hold-up both on trays and in downcomers as well as hydraulic constraints can be applied to systematically design industrial RD plate columns to simultaneously obtain optimal operating variables and equipment structure variables.

Predictive Controller for Large-Scale Fuzzy Polynomial Systems

This paper presents an innovative method to tackle the predictive-control challenges associated with large-scale fuzzy polynomial systems comprising interconnected polynomial fuzzy systems. This study models large-scale nonlinear fuzzy systems in a polynomial framework, which can reduce the number of fuzzy rules. We derive the conditions for controller synthesis in the main theorem using the Lyapunov theory and sum-of-squares technique. Simulation results confirm the validity and efficiency of this approach.

Hybrid Hu-Storey type methods for large-scale nonlinear monotone systems and signal recovery

We propose two hybrid methods for solving large-scale monotone systems, which are based on derivative-free conjugate gradient approach and hyperplane projection technique. The conjugate gradient approach is efficient for large-scale systems due to low memory, while projection strategy is suitable for monotone equations because it enables simply globalization. The derivative-free function-value-based line search is combined with Hu-Storey type search directions and projection procedure, in order to construct globally convergent methods. Furthermore, the proposed methods are applied into solving a number of large-scale monotone nonlinear systems and reconstruction of sparse signals. Numerical experiments indicate the robustness of the proposed methods.

Advancing large-scale thin-film PPLN nonlinear photonics with segmented tunable micro-heaters

Thin-film periodically poled lithium niobate (TF-PPLN) devices have recently gained prominence for efficient wavelength conversion processes in both classical and quantum applications. However, the patterning and poling of TF-PPLN devices today are mostly performed at chip scales, presenting a significant bottleneck for future large-scale nonlinear photonic systems that require the integration of multiple nonlinear components with consistent performance and low cost. Here, we take a pivotal step towards this goal by developing a wafer-scale TF-PPLN nonlinear photonic platform, leveraging ultraviolet stepper lithography and an automated poling process. To address the inhomogeneous broadening of the quasi-phase matching (QPM) spectrum induced by film thickness variations across the wafer, we propose and demonstrate segmented thermal optic tuning modules that can precisely adjust and align the QPM peak wavelengths in each section. Using the segmented micro-heaters, we show the successful realignment of inhomogeneously broadened multi-peak QPM spectra with up to 57% enhancement of conversion efficiency. We achieve a high normalized conversion efficiency of 3802% W−1 cm−2 in a 6 mm long PPLN waveguide, recovering 84% of the theoretically predicted efficiency in this device. The advanced fabrication techniques and segmented tuning architectures presented herein pave the way for wafer-scale integration of complex functional nonlinear photonic circuits with applications in quantum information processing, precision sensing and metrology, and low-noise-figure optical signal amplification.

Extinction Chains Reveal Intermediate Phases Between the Safety and Collapse in Mutualistic Ecosystems

Ecosystems are undergoing unprecedented persistent deterioration due to unsustainable anthropogenic human activities, such as overfishing and deforestation, and the effects of such damage on ecological stability are uncertain. Despite recent advances in experimental and theoretical studies on regime shifts and tipping points, theoretical tools for understanding the extinction chain, which is the sequence of species extinctions resulting from overexploitation, are still lacking, especially for large-scale nonlinear networked systems. In this study, we developed a mathematical tool to predict regime shifts and extinction chains in ecosystems under multiple exploitation situations and verified it in 26 real-world mutualistic networks of various sizes and densities. We discovered five phases during the exploitation process: safe, partial extinction, bistable, tristable, and collapse, which enabled the optimal design of restoration strategies for degraded or collapsed systems. We validated our approach using a 20-year dataset from an eelgrass restoration project. Counterintuitively, we also found a specific region in the diagram spanning exploitation rates and competition intensities, where exploiting more species helps increase biodiversity. Our computational tool provides insights into harvesting, fishing, exploitation, or deforestation plans while conserving or restoring the biodiversity of mutualistic ecosystems.

A Semi-Global Finite-Time Decentralized Control Method for High-Order Large-Scale Nonlinear Systems

This study focuses on the decentralized stabilization issue of high-order large-scale nonlinear systems with unknown disturbances. A novel decentralized semi-global finite-time control approach is suggested by constructing a Lyapunov function with both quadratic and higher-order components and employing the method of homogeneous domination. Based on the designed Lyapunov function, a state-feedback controller is constructed for the nominal system. Subsequently, the scaling gain is flexibly introduced to enable semi-globally finite-time stabilization of the nonlinear system. Besides, the approach is extended to the problem of decentralized tracking control of high-order large-scale nonlinear systems. Finally, numerical and practical examples validate the effectiveness of the presented control strategy.

Energetic spectral-element time marching methods for phase-field nonlinear gradient systems

We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen–Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method. Different from other spectral methods in time using spectral Petrov-Galerkin or weighted Galerkin approximations, the presented implicit method employs an energetic variational Galerkin form that can maintain the mass conservation and energy dissipation property of the continuous dynamical system. Another advantage of this method is its superconvergence. A high-order extrapolation is adopted for the nonlinear term to get the semi-implicit method. The semi-implicit method does not have superconvergence, but can be improved by a few Picard-like iterations to recover the superconvergence of the implicit method. Numerical experiments verify that the method using Legendre elements of degree three outperforms the 4th-order implicit-explicit backward differentiation formula and the 4th-order exponential time difference Runge-Kutta method, which were known to have best performances in solving phase-field equations. In addition to the standard Allen–Cahn equation, we also apply the method to a conservative Allen–Cahn equation, in which the conservation of discrete total mass is verified. The applications of the proposed methods are not limited to phase-field Allen–Cahn equations. They are suitable for solving general, large-scale nonlinear dynamical systems.

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Decentralized Implicit Inverse Control for Large-Scale Hysteretic Nonlinear Time-Delay Systems and Its Application on Triple-Axis Giant Magnetostrictive Actuators.

This article proposes fuzzy-logic systems (FLSs)-based decentralized adaptive implicit inverse control scheme for a class of large-scale nonlinear systems with time delays and multihysteretic loops. Our novel algorithms feature hysteretic implicit inverse compensators designed to effectively mitigate multihysteretic loops in large-scale systems. In this article, hysteretic implicit inverse compensators can replace the traditional hysteretic inverse models, which are exceedingly difficult to construct, and no longer necessary. The authors provide three contributions: 1) a searching mechanism to obtain the approximate value of the practical input signal from the so-called hysteretic temporary control law; 2) the arbitrarily small L∞ norm of the tracking error attained by utilizing the proposed initializing technique, which applies the combination of FLSs and a finite covering lemma to deal with time delays; and 3) the construction of a triple-axis giant magnetostrictive motion control platform, which validates the effectiveness of the proposed control scheme and algorithms.

A Hierarchical approach for isolating sensor faults from un-stealthy attacks in large-scale systems

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L2−L∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (CSTR).

Composite adaptive exponential tracking control for large-scale nonlinear systems with sensor faults

The issue of composite adaptive exponential tracking control for a class of large-scale nonlinear systems under model uncertainties, external disturbances, along with multiplicative and additive time-varying sensor faults is considered in this paper. The command filtered backstepping approach is employed to address the “explosion of terms” issue inherent in standard backstepping method. A novel compensating system is incorporated to mitigate the effects of filtering errors and enhance the convergence of tracking errors. The composite estimation laws are designed by integrating the compensated tracking errors, prediction errors stemming from output estimators, along with the proportional and integral estimation errors of faulty terms. This on-line estimation framework enables achieving fast, robust and accurate estimation, even when employing low learning and modification gains. By incorporating modification terms with appropriate time-varying gains, it is demonstrated that the resulting system is globally exponentially stable. Finally, the effectiveness of the presented FTC approach is illustrated through two simulation examples.

Wafer-Scale Periodic Poling of Thin-Film Lithium Niobate.

Periodically poled lithium niobate on insulator (PPLNOI) offers an admirably promising platform for the advancement of nonlinear photonic integrated circuits (PICs). In this context, domain inversion engineering emerges as a key process to achieve efficient nonlinear conversion. However, periodic poling processing of thin-film lithium niobate has only been realized on the chip level, which significantly limits its applications in large-scale nonlinear photonic systems that necessitate the integration of multiple nonlinear components on a single chip with uniform performances. Here, we demonstrate a wafer-scale periodic poling technique on a 4-inch LNOI wafer with high fidelity. The reversal lengths span from 0.5 to 10.17 mm, encompassing an area of ~1 cm2 with periods ranging from 4.38 to 5.51 μm. Efficient poling was achieved with a single manipulation, benefiting from the targeted grouped electrode pads and adaptable comb line widths in our experiment. As a result, domain inversion is ultimately implemented across the entire wafer with a 100% success rate and 98% high-quality rate on average, showcasing high throughput and stability, which is fundamentally scalable and highly cost-effective in contrast to traditional size-restricted chiplet-level poling. Our study holds significant promise to dramatically promote ultra-high performance to a broad spectrum of applications, including optical communications, photonic neural networks, and quantum photonics.

Dynamic event-triggered control of large-scale nonlinear systems with sensor uncertainty

In this article, the dynamic event-triggered control problem is investigated for a class of large-scale nonlinear systems subject to sensor uncertainty. The unknown nonlinearities involved in each subsystem are assumed to be bounded by time-varying continuous functions multiplied by unknown constants and unmeasured states. To estimate the unmeasured states of each subsystem, a time-varying high-gain observer is constructed. Then, a dynamic event-triggered mechanism is proposed by introducing an internal dynamic variable in triggering function. Combined with the dual-domination approach, a dynamic event-triggered output feedback controller is developed for each subsystem. Subsequently, it is proved the convergence of all states is ensured based on the Lyapunov theory and the Zeno behavior can be avoided. Eventually, an example is presented to demonstrate the effectiveness of the proposed dynamic event-triggered control scheme.

Event-based adaptive active disturbance rejection control for nonlinear large-scale systems with input delay

This paper explores the active disturbance rejection control (ADRC) issue for interconnected large-scale systems with unmeasured states, input delay and a total disturbance composed of unknown constrained external disturbances. An enhanced extended state observer is built via fuzzy logic systems to identify system uncertainties and states and keep restraining the total disturbance of uncertain systems. When the triggering condition is met, the tracking differentiator component of the ADRC is able to reduce the communication overhead by successfully applying the backstepping control approach and the dynamic event-triggered mechanism. Meanwhile, the integral compensation method eliminates the negative effect cased by the input delay. Furthermore, the developed decentralised fuzzy control scheme can ensure that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded and Zeno behaviour does not occurs. Finally, an example is used to depict the validity of the control approach.

Multi-level optimization strategies for large-scale nonlinear process systems

With growing needs to develop and improve climate-friendly processes, optimization strategies are essential at all levels of decision-making in chemical and energy processes, including process development, process synthesis and design, as well as process operations, control, scheduling, and planning. Challenges include the formulation of well-posed and well-conditioned process models, and development and application of efficient, reliable optimization algorithms. Here we describe a synthesis of optimization concepts and algorithms that enable large-scale nonlinear programming, nonintrusive decomposition strategies and the inclusion of a wide class of surrogate models. All of these are crucial to address challenging nonconvex, multi-scale problems in Computer Aided Process Engineering (CAPE). These elements are demonstrated through dynamic optimization strategies for novel energy generation, demand-based optimization for specialty chemicals, and optimization with integrated heterogeneous models for carbon capture processes.

Structured interpolation for multivariate transfer functions of quadratic-bilinear systems

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting large-scale nonlinear systems. The high dimensionality of the dynamics causes computational bottlenecks, especially when these large-scale systems need to be simulated for a variety of situations such as different forcing terms. This motivates model reduction where the goal is to replace the full-order dynamics with accurate reduced-order surrogates. Interpolation-based model reduction has been proven to be an effective tool for the construction of cheap-to-evaluate surrogate models that preserve the internal structure in the case of weak nonlinearities. In this paper, we consider the construction of multivariate interpolants in frequency domain for structured quadratic-bilinear systems. We propose definitions for structured variants of the symmetric subsystem and generalized transfer functions of quadratic-bilinear systems and provide conditions for structure-preserving interpolation by projection. The theoretical results are illustrated using two numerical examples including the simulation of molecular dynamics in crystal structures.

Adaptive Decentralized Fuzzy Resilient Control for Large-Scale Nonlinear Systems Against Stochastic Disturbances and DoS Attacks

Adaptive Decentralized Fuzzy Resilient Control for Large-Scale Nonlinear Systems Against Stochastic Disturbances and DoS Attacks

A dual-gain scaling approach to event-triggered adaptive tracking for large-scale nonlinear systems via output feedback

A novel non-backstepping output feedback control approach, called as the dual-gain scaling approach, is proposed by combining the extended Lyapunov matrix inequalities with dual-domination idea. This approach provides partially decentralised adaptive output feedback controllers with three event-triggered mechanisms to achieve the global practical tracking of a family of uncertain large-scale nonlinear systems subject to unknown control coefficients and strongly interconnected nonlinearities with output-polynomial growth rate. The dual gains are embedded in the observers and controllers, which can effectively compensate for time-varying control coefficients and unknown constant growth rate multiplied by output-polynomial function. Three different threshold schemes including fixed threshold, relative threshold and time-varying threshold are introduced to save communication resources. The stability analysis shows that the solutions of the closed-loop system are globally uniformly bounded and the tracking error converges to a preset compact set after a finite time; also, there will be no zeno behaviour in the closed-loop response.

Adaptive Fuzzy Echo State Network Control of Fractional-Order Large-Scale Nonlinear Systems With Time-Varying Deferred Constraints

Adaptive Fuzzy Echo State Network Control of Fractional-Order Large-Scale Nonlinear Systems With Time-Varying Deferred Constraints